Abstract
Topological quantum phases cannot be characterized by Ginzburg–Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable.
Highlights
We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges
We show that the topological polaron (TP) Chern number, discussed in the protocol above, is given by the inverse of the fractional qp charge eà 1⁄4 e/m (e is the charge of particles in the host many-body system), CTP
Using internal degrees of freedom of the impurity, fully coherent control can be gained over individual qp excitations of the host many-body system
Summary
The integer and fractional quantum Hall effects[1,2,3] in contrast are examples of quantum phases of matter, for which no local order parameters exist. Instead, these systems are described by nonlocal topological invariants[4]. Our method is ideally suited to systems of ultracold atoms, which recently emerged as a new promising platform for realizing and probing various topological states of matter. The Chern number has been measured in transport experiments[29] and the celebrated Haldane model has been realized[30] in systems of weakly interacting ultracold atoms. Direct and fully coherent control over individual atoms has been demonstrated in experiments with ultracold quantum gases, see, for example, refs 37,38
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